1. What is the Prandtl Number?

The Prandtl number (Pr) is a dimensionless number that relates momentum diffusivity (kinematic viscosity) to thermal diffusivity. For water, it helps characterize the relative thickness of the velocity boundary layer to the thermal boundary layer.

2. How Does the Calculator Work?

The calculator uses the Prandtl number equation:

Where:

• \( \mu \) — Dynamic viscosity (Pa·s)
• \( c_p \) — Specific heat capacity (J/kg·K)
• \( k \) — Thermal conductivity (W/m·K)

Explanation: The equation shows the ratio of momentum diffusivity to thermal diffusivity, indicating how quickly momentum transfers relative to heat.

3. Importance of Prandtl Number

Details: The Prandtl number is crucial in heat transfer calculations, particularly in convective heat transfer problems. It helps determine the relative effectiveness of momentum and energy transport by diffusion.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, specific heat capacity in J/kg·K, and thermal conductivity in W/m·K. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical Prandtl number for water?
A: For water at 20°C, Pr ≈ 7.0. It decreases with increasing temperature (≈1.75 at 100°C).

Q2: What does a high Prandtl number indicate?
A: High Pr (>1) means momentum diffuses faster than heat (thermal boundary layer is thicker than velocity boundary layer).

Q3: What are the units of Prandtl number?
A: Prandtl number is dimensionless - all units cancel out in the calculation.

Q4: How does Prandtl number affect heat transfer?
A: Higher Pr fluids (like oils) have thicker thermal boundary layers, affecting convection heat transfer coefficients.

Q5: Can this calculator be used for other fluids?
A: Yes, the equation is universal, but the input values must be for the specific fluid you're analyzing.